Of course, it is entirely possible for Microsoft to offer Xbox Live for free and still make a profit. They just wouldn't make as much of a profit. And a business logically wants to maximize its profits (that, I remind you, is the point of a business - to make money for investors).
Is paying for it a bad thing? If you think it's worth it, and if you find you get your money's worth, then no, it's not a bad thing. If you like the service and you find the price reasonable, then it's not bad at all. If you do find it unreasonable and you don't derive enjoyment from the service then, uh, I suppose, don't pay for it? I do believe that's an option, if I'm not mistaken. It's not like there's a gun held to your head demanding that you buy it. It's not like you need Xbox Live. I'm pretty sure, according to most people that I've talked to, that Xbox live is not a requirement for a happy life. So if you think it's not worth the money, and this is just a suggestion mind you, you might not want to pay for it.
Should it be free? Well, here's another question: A Porsche Panamera S costs about 260,000 dollars. It certainly doesn't cost that much to make. Not by a mile. Should you angrily demand, shout and coerce the porsche dealer to lower the price by 50,000 dollars? Is anyone entitled to an immediate discount, merely because it doesn't cost that much to make? No! It's a completely optional luxury car!
Xbox live is a completely optional luxury gaming service that really, really isn't that important in the scheme of things. You say it should be free. Why? Are you being horribly oppressed by the fact that it is not free? Are you suffering immensely under the burden of paying for Xbox Live? Has your household budget been ruined and your family shattered by the fact that a completely optional multiplayer gaming service was not offered for free? No? Well keep following that line of thought.
You are well entitled to think that it is not worth the price. I don't think Xbox Live is worth the price myself. And you know what I do about it? I don't purchase a gold membership! That's all I had to do - not buy something, and so far, I appear to be alive, happy, healthy and in possession of everything I need to live a good life.